What is the smallest planetary mass that can prevent 'me' from flying off into space?

I have a series of astronauts landing on an asteroid. I'd like to know the threshold of mass for them to not fly off into space. Specifications:

• Assumption is all astronauts are under 180cm, 80kg.
• Assumption is an astronaut may jump lightly and not fly off into space.
• Request is a comfortable radius of said asteroid, which has an average density of 2 g/cm³ (pretty dense), with a mostly spheroid shape.
• Weight and height includes equipment (this is far future); astronauts are fit.

In my story I'd like to see my astronauts be able to jump up into the 'sky,' but able to come back down without flying out forever.

If there are other factors I should include, please let me know. Also, I will accept a magnitude-of-order rather than an impossibly precise answer (thus not hard-science).

EDIT: AND I KNOW THIS AFFECTS THE ANSWER - 80kg, not 30kg. I will still accept the best answer if it used 30kg due to my error, but showed the math.

posted almost 8 years ago

Mikey‭

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